"Pupils’ education is being damaged as a result of them being packed into schools like sardines."

Some schools have been desperately attempting to build new sites over the summer, whilst others are will be putting on classes of more than 30 pupils, despite previous attempts to ban the practice.

Councils have also started creating “Titan” schools with 1,000-plus children, sacrificing playgrounds and green spaces for temporary classrooms.

“Split-shift” schools have been set up with double intakes studying at different times during an extended school day and week.

But despite the drastic steps hundreds of children due to be starting school for the first time are still without place and almost one in ten – more than 50,000 – are going to a primary that was not their family’s first choice.

A Department for Education spokesman said: ‘We are spending £5billion by 2015 on creating new school places – more than double the amount spent by the previous government in the same time frame.’

London Councils, representing 33 local authorities, yesterday estimated a funding shortfall of £1.04billion to create sufficient school places by 2016/17.

In total 26 local authorities responded to requests for information about their plans for primary schools for the new terms.

The news comes months after a warning from the National Audit Office that 240,000 extra primary places would be needed by September next year.